About How Good is Estimation? Assessment Materials Page 1 of 12

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1 About How Good is Estimation? Assessment Name: Multiple Choice. 1 point each. 1. Which unit of measure is most appropriate for the area of a small rug? a) feet b) yards c) square feet d) square yards 2. Which unit of measure is most appropriate for the perimeter of a park? a) centimeters b) meters c) square centimeters d) square meters 3. The perimeter of Mr. Hodgman s yard is measured and found to be 450 feet. He would like to put up a wire fence, but the wire is sold by the yard. How many yards does Mr. Hodgman need to buy? a) 45 yards b) 50 yards c) 150 yards d) 1350 yards 4. Ms. Neitzel has a dog kennel that is 24 square yards in area. If she had measured using the metric system, about how many square meters in area is the dog kennel? a) 8 m 2 b 20 m 2 c) m 2 d) 24 m 2 5. The dimensions of an Olympic-sized Pool are required to be 25 meters by 50 meters. The pool maintenance company would like to make a cover for the pool, but the material is sold in yards. About how much material is needed to cover the pool? a) 12.5 square yards b) 150 square yards c) 1300 square yards d) 1500 square yards 6. Which of the following situations would NOT require a level of precision higher than estimation? a) the pennies in my piggy bank b) dosage for medicine c) the tax taken out of a paycheck d) number of balls to fill a ball pit About How Good is Estimation? Assessment Materials Page 1 of 12

2 Short Answer. 2 points each. 7. Shannon needs to buy tiles for a kitchen countertop. The countertop length is 8 feet and the width is 3 feet 5 inches. She will use 3-inch square tiles to cover the countertop and create a backsplash against the wall on three sides. The backsplash will be one tile high and run along one of the long sides and both of the shorter sides. There will be a ¼ inch grout line between each tile. To help Shannon create a budget and compare prices at different home improvement stores, you need to: estimate the number of tiles she needs to buy explain the level of precision needed support your answer with words, numbers, and/or diagrams About How Good is Estimation? Assessment Materials Page 2 of 12

3 8. Joe and Sandy are replacing the carpet in their living room. Joe believes the first thing they need to do is get a precise measurement of the area of the living room. Sandy believes that an estimate would be appropriate measurement for this situation. Decide who you think is right and explain your reasoning. About How Good is Estimation? Assessment Materials Page 3 of 12

4 9. Mr. Hodgman wants to cover his triangular garden with beauty bark. The base of the triangle is 16 feet, 9 inches and the height of the triangle is 12 feet, 4 inches. A bag of beauty bark covers about 1 square yard of area. How many bags will Mr. Hodgman need to buy? Show all your work, including words, numbers and diagrams to help communicate your thinking. Mr. Hodgman needs to buy bags of beauty bark. About How Good is Estimation? Assessment Materials Page 4 of 12

5 Extended Response. 4 points. 10. Kara, Sally, Alex and Jack just inherited a piece of land. They must determine how to divide the land equally between the four of them. They have come to you for help in developing a plan. Write a plan that describes a process to divide the land equally among the four of them. Be sure to include in your plan: The process of measurement of the land The process of dividing the land equally The units of measurement and your reason for this choice The degree of precision needed and why that level is needed About How Good is Estimation? Assessment Materials Page 5 of 12

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7 Multiple Choice. 1 point each. About How Good is Estimation? Assessment Solutions & Rubrics 1. Which unit of measure is most appropriate for the area of a small rug? a) feet (appropriate size, but linear, not area) b) yards (too big and linear unit of measure, not area) c) square feet d) square yards (appropriate dimension, but too big) 2. Which unit of measure is most appropriate for the perimeter of a park? a) centimeters (appropriate dimension, but too small) b) meters c) square centimeters (dimension and size inappropriate) d) square meters (size is appropriate, but the dimension is not) 3. The perimeter of Mr. Hodgman s yard is measured and found to be 450 feet. He would like to put up a wire fence, but the wire is sold by the yard. How many yards does Mr. Hodgman need to buy? a) 45 yards (divided by 10 thinking metric change) b) 50 yards (divided by 9 thinking area change) c) 150 yards d) 1350 yards (multiplied by 3 instead of dividing) 4. Ms. Neitzel has a dog kennel that is 24 square yards in area. If she had measured using the metric system, about how many square meters in area is the dog kennel? a) 8 m 2 (divided by 3, thinking yards feet) b) 20 m 2 (Calculated, then rounded down) c) m 2 (Calculated exactly, not an estimate) d) 24 m 2 5. The dimensions of an Olympic-sized Pool are required to be 25 m by 50 m. If the pool maintenance company would like to make a cover for the pool, but the material is sold in yards. About how much material is needed to cover the pool? a) 12.5 square yards (divided each by 10 thinking metric conversion) b) 150 square yards (estimated perimeter) c) 1300 square yards d) 1500 square yards (did not estimate, converted and then rounded) 6. Which of the following situations would NOT require a level of precision higher than estimation? a) the pennies in my piggy bank (should be counted precisely) b) dosage for medicine (should be measured precisely) c) the tax taken out of a paycheck (should be calculated precisely) d) number of balls to fill a ball pit About How Good is Estimation? Assessment Materials Page 7 of 12

8 Short Answer. 2 points each. 7. Shannon needs to buy tiles for a kitchen countertop. The countertop length is 8 feet and the width is 3 feet 5 inches wide. She will use 3-inch square tiles to cover the countertop and create a backsplash against the wall on three sides. The backsplash will be one tile high and run along one of the long sides and both of the shorter sides. There will be a ¼ inch grout line between each tile. To help Shannon create a budget and compare prices at different home improvement stores, you need to: Estimate the number of tiles she needs to buy Explain the level of precision needed Support your answer with words, numbers, and/or diagrams Area of the countertop is 8 ft * 3.5 ft (rounding) = 28 square feet Convert to square inches by multiplying by * 144 = 4032 sq. in. Each tile has an area of 9 square inches. The countertop requires (4032/9) 448 tiles. Backsplash is 8 ft + 2*3.5 ft = 15 feet in length There are 4 tiles per linear foot, so there will need to be 4*15 = 60 tiles in the backsplash. You would need to buy 508 tiles, but you might want to buys a few extra in case some break. You would want to ignore the grout lines because you want to make sure to have extras, and you are only getting an estimate at this point. About How Good is Estimation? Assessment Materials Page 8 of 12

9 ME02 (Units and Systems) demonstrate understanding of how to convert within the US or metric system to achieve an appropriate level of precision; Item Characteristics: Items may ask students to convert a unit of measurement within a system to achieve an appropriate level of precision in a given situation. 2-point response: The student shows an understanding of converting a unit of measurement within a system to achieve an appropriate level of precision in a given situation by doing the following: finding number of tiles needed for the countertop and the backsplash by calculating area, converting to feet to inches or inches to feet, and dividing appropriately. discussing the level of precision by stating that this is an initial estimation so it does not need to be exact. A response may include information about ignoring the grout, measurements should be rounded up and/or that extra tiles may be purchased. 1-point response: The student shows partial understanding how to estimate area and determine an appropriate level of precision by doing one of the following: attempting to find number of tiles needed for the countertop and the backsplash by calculating area, converting to feet to inches or inches to feet, and dividing appropriately, but completing several errors directly related to conversion. minimal or no explanation about the level of precision is present. 0-point response: The student shows very little or no understanding converting units or necessary levels of precision. About How Good is Estimation? Assessment Materials Page 9 of 12

10 8. Joe and Sandy are replacing the carpet in their living room. Joe believes the first thing they need to do is get a precise measurement of the area of the living room. Sandy believes that an estimate would be appropriate measurement for this situation. Decide who you think is right and explain your reasoning. Answers will vary. Student that choose Joe need to explain that it would be beneficial to get a precise measurement so that they know exactly how much carpet they need. This would prevent buying too little and having a gap or buying too much and spending more money than was needed. Students also may mention that it might be a good idea to buy extra, but that this is not estimating. Students that choose Sandy need to explain that at the beginning of a process estimation is appropriate to help you set a budget. Students may discuss over estimating so that there will be leftovers. ME04 (Estimated Measurements) Identify situations in which estimated measurements are sufficient; use estimation to obtain reasonable measurements at an appropriate level of precision. Item Characteristics: Items may ask students to determine when or whether estimation is appropriate for finding approximations of a measurement and explain why they would use estimation rather than a precise measurement. 2-point response: The student shows an understanding of when estimation is an appropriate measurement by choosing a position and defending it either by stating that estimation is appropriate to help you make a budget or stating that estimation is not appropriate because they will need to have exact measurements so they do not run out or pay too much. 1-point response: The student shows partial understanding of when estimation is an appropriate measurement by choosing a position but providing little or no explanation of their reasoning. 0-point response: The student shows very little or no understanding of when estimation is an appropriate measurement. This response would include answers that have contradictory statements and no response. About How Good is Estimation? Assessment Materials Page 10 of 12

11 9. Mr. Hodgman wants to cover his triangular garden with beauty bark. The base of the triangle is 16 feet, 9 inches and the height of the triangle is12 feet, 4 inches. A bag of beauty bark covers about 1 square yard of area. How many bags will Mr. Hodgman need to buy? Show all your work, including words, numbers and diagrams to help communicate your thinking. Base of the triangle = 16 9/12 feet or ft Height of the triangle = 12 4/12 feet or ft Area of the triangle = (16.75*12.25)/2 = sq. ft There are 3 feet in each yard. So, /9 = sq. yards in his garden. Students may round up to account for the fact that you cannot buy a part of a bag or may round down and say that they could spread it a little thinner to make up for the 0.39 sq. yards. Mr. Hodgman needs to buy _11 or 12_ bags of beauty bark. ME02 (Units and Systems) demonstrate understanding of how to convert within the US or metric system to achieve an appropriate level of precision. Item Characteristics: Items may ask students to convert a unit of measurement within a system to achieve an appropriate level of precision in a given situation. 2-point response: The student shows an understanding of how to convert within a system by appropriately changing inches to feet accurately converting from feet to yards or square feet to square yards in order to obtain the answer of 11 or 12 bags. Students may make one minor mathematical error not related to conversion. 1-point response: The student shows partial understanding of how to convert within a system by completing two of the following: changing inches to feet with some errors, such as writing 16.9 feet. attempting to convert square feet to square yards with error, such as dividing by 3. Students may make two or three minor mathematical errors not related to conversion. 0-point response: The student shows very little or no understanding of how to convert within a system by completing. About How Good is Estimation? Assessment Materials Page 11 of 12

12 Extended Response. 4 points. 10. Sara, Sally, Jeff and Jack just inherited a piece of land. They must determine how to divide the land equally and fairly between the four of them. They have come to your for help in developing a plan. In your plan be sure to include the process of measurement, the units of measurement and the degree of precision needed. SR04 (Construct Solutions and Verify Results) Use viable strategies and appropriate concepts and procedures to construct a solution. Item Characteristics: Items may ask students to use various concepts, procedures, and problem solving to construct a solution for a given situation and then to explain why the solution is appropriate and/or make a comparison using evidence and information from the problem situation, known facts, patterns, relationships, counter-examples, and proportional reasoning. 4-point response: The student shows an understanding of developing a procedure for measuring an area and selecting the appropriate level of precision by doing the following: describing a process to find the area of the land describe the process for dividing the area into four equal parts selecting an appropriate unit to maintain fairness, such as feet discussing the level of precision, accurately measuring to the foot/inch 3-point response includes three of the four listed above. 2-point response includes two of the four listed above. 1-point response includes one of the four listed above. 0-point response: The student shows very little or no understanding About How Good is Estimation? Assessment Materials Page 12 of 12